Question

In a regular polygon, any interior angle exceeds the exterior angle by 120 degrees. Then, the number of diagonals of this polygon is

• A. 30
• B. 54
• C. 64
• D. None of Above

Answer 1

Answer: (B)

54

Answer 2

A polygon with 'n' sides can be expressed as having an inner angle sum of $(2n−4)× 90$ and an external angle sum of 360 degrees.
Consequently, $120\times n$
$⇒ (2n−4)90−360=120n$
$⇒ 60n = 720$
$⇒ n = 12$ will be the difference between them.
We are aware that a regular polygon has $^nC_2 - n = ^{12}C_2 - 12 = 66 - 12 = 54$ diagonals.
The correct answer is (B): 54.